It is known from EP 0 358 496 B2 to measure dimensions of a wheel, especially a vehicle wheel by means of ultrasonic sensors scanning the wheel surface or a part of the wheel surface. The ultrasonic sensors are mounted on a pivot member and, during the measurement, the ultrasonic sensors pivot about a pivot axis by means of the pivot member. For the detection of the angular position of the pivot member, a rotary type potentiometer is connected via transmission means to the pivot member.